Find the Exact Value cot((5pi)/2)

Problem

cot((5*π)/2)

Solution

1. Identify the definition of the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Substitute the given angle θ=(5*π)/2 into the expression.

cot((5*π)/2)=cos((5*π)/2)/sin((5*π)/2)

3. Find the coterminal angle by subtracting multiples of 2*π to locate the angle on the unit circle.

(5*π)/2−2*π=(5*π)/2−(4*π)/2

(5*π)/2−(4*π)/2=π/2

4. Evaluate the sine and cosine values at the coterminal angle π/2

cos((5*π)/2)=cos(π/2)=0

sin((5*π)/2)=sin(π/2)=1

5. Calculate the final ratio.

0/1=0

Final Answer

cot((5*π)/2)=0

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